0.10/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.10/0.12	% Command    : tptp2X_and_run_prover9 %d %s
0.12/0.32	% Computer   : n018.cluster.edu
0.12/0.32	% Model      : x86_64 x86_64
0.12/0.32	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.32	% Memory     : 8042.1875MB
0.12/0.32	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.32	% CPULimit   : 180
0.12/0.32	% DateTime   : Thu Aug 29 09:19:22 EDT 2019
0.12/0.33	% CPUTime    : 
0.84/1.15	============================== Prover9 ===============================
0.84/1.15	Prover9 (32) version 2009-11A, November 2009.
0.84/1.15	Process 24319 was started by sandbox on n018.cluster.edu,
0.84/1.15	Thu Aug 29 09:19:22 2019
0.84/1.15	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 180 -f /tmp/Prover9_23880_n018.cluster.edu".
0.84/1.15	============================== end of head ===========================
0.84/1.15	
0.84/1.15	============================== INPUT =================================
0.84/1.15	
0.84/1.15	% Reading from file /tmp/Prover9_23880_n018.cluster.edu
0.84/1.15	
0.84/1.15	set(prolog_style_variables).
0.84/1.15	set(auto2).
0.84/1.15	    % set(auto2) -> set(auto).
0.84/1.15	    % set(auto) -> set(auto_inference).
0.84/1.15	    % set(auto) -> set(auto_setup).
0.84/1.15	    % set(auto_setup) -> set(predicate_elim).
0.84/1.15	    % set(auto_setup) -> assign(eq_defs, unfold).
0.84/1.15	    % set(auto) -> set(auto_limits).
0.84/1.15	    % set(auto_limits) -> assign(max_weight, "100.000").
0.84/1.15	    % set(auto_limits) -> assign(sos_limit, 20000).
0.84/1.15	    % set(auto) -> set(auto_denials).
0.84/1.15	    % set(auto) -> set(auto_process).
0.84/1.15	    % set(auto2) -> assign(new_constants, 1).
0.84/1.15	    % set(auto2) -> assign(fold_denial_max, 3).
0.84/1.15	    % set(auto2) -> assign(max_weight, "200.000").
0.84/1.15	    % set(auto2) -> assign(max_hours, 1).
0.84/1.15	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.84/1.15	    % set(auto2) -> assign(max_seconds, 0).
0.84/1.15	    % set(auto2) -> assign(max_minutes, 5).
0.84/1.15	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.84/1.15	    % set(auto2) -> set(sort_initial_sos).
0.84/1.15	    % set(auto2) -> assign(sos_limit, -1).
0.84/1.15	    % set(auto2) -> assign(lrs_ticks, 3000).
0.84/1.15	    % set(auto2) -> assign(max_megs, 400).
0.84/1.15	    % set(auto2) -> assign(stats, some).
0.84/1.15	    % set(auto2) -> clear(echo_input).
0.84/1.15	    % set(auto2) -> set(quiet).
0.84/1.15	    % set(auto2) -> clear(print_initial_clauses).
0.84/1.15	    % set(auto2) -> clear(print_given).
0.84/1.15	assign(lrs_ticks,-1).
0.84/1.15	assign(sos_limit,10000).
0.84/1.15	assign(order,kbo).
0.84/1.15	set(lex_order_vars).
0.84/1.15	clear(print_given).
0.84/1.15	
0.84/1.15	% formulas(sos).  % not echoed (64 formulas)
0.84/1.15	
0.84/1.15	============================== end of input ==========================
0.84/1.15	
0.84/1.15	% From the command line: assign(max_seconds, 180).
0.84/1.15	
0.84/1.15	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.84/1.15	
0.84/1.15	% Formulas that are not ordinary clauses:
0.84/1.15	1 (all U all V (strictly_less_than(U,V) <-> less_than(U,V) & -less_than(V,U))) # label(stricly_smaller_definition) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	2 (all U less_than(U,U)) # label(reflexivity) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	3 (all U all V (less_than(U,V) | less_than(V,U))) # label(totality) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	4 (all U all V all W (less_than(V,W) & less_than(U,V) -> less_than(U,W))) # label(transitivity) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	5 (all U less_than(bottom,U)) # label(bottom_smallest) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	6 (all U all V (issmallestelement_pq(U,V) & contains_pq(U,V) -> U = findmin_pq_eff(U,V))) # label(ax13) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	7 (all U all V remove_pq(insert_pq(U,V),V) = U) # label(ax11) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	8 (all U all V (issmallestelement_pq(U,V) & contains_pq(U,V) -> removemin_pq_res(U,V) = V)) # label(ax16) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	9 (all U all V ((all W (contains_pq(U,W) -> less_than(V,W))) <-> issmallestelement_pq(U,V))) # label(ax10) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	10 (all U all V (issmallestelement_pq(U,V) & contains_pq(U,V) -> remove_pq(U,V) = removemin_pq_eff(U,V))) # label(ax15) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	11 (all U all V (issmallestelement_pq(U,V) & contains_pq(U,V) -> V = findmin_pq_res(U,V))) # label(ax14) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	12 (all U all V all W (W = V | contains_pq(U,W) <-> contains_pq(insert_pq(U,V),W))) # label(ax9) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	13 (all U all V isnonempty_pq(insert_pq(U,V))) # label(ax7) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	14 (all U all V all W (contains_pq(U,W) & W != V -> remove_pq(insert_pq(U,V),W) = insert_pq(remove_pq(U,W),V))) # label(ax12) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	15 (all U -contains_pq(create_pq,U)) # label(ax8) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	16 (all U all V all W insert_pq(insert_pq(U,V),W) = insert_pq(insert_pq(U,W),V)) # label(ax17) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	17 (all U all V all W lookup_slb(insert_slb(U,pair(V,W)),V) = W) # label(ax26) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	18 (all U all V all W all X (V = W | contains_slb(U,W) <-> contains_slb(insert_slb(U,pair(V,X)),W))) # label(ax21) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	19 (all U all V all W isnonempty_slb(insert_slb(U,pair(V,W)))) # label(ax19) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	20 (all U create_slb = update_slb(create_slb,U)) # label(ax28) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	21 (all U all V all W remove_slb(insert_slb(U,pair(V,W)),V) = U) # label(ax24) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	22 (all U all V all W all X (contains_slb(U,W) & V != W -> insert_slb(remove_slb(U,W),pair(V,X)) = remove_slb(insert_slb(U,pair(V,X)),W))) # label(ax25) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	23 (all U all V all W all X (strictly_less_than(X,W) -> insert_slb(update_slb(U,W),pair(V,W)) = update_slb(insert_slb(U,pair(V,X)),W))) # label(ax29) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	24 (all U all V all W all X (less_than(W,X) -> update_slb(insert_slb(U,pair(V,X)),W) = insert_slb(update_slb(U,W),pair(V,X)))) # label(ax30) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	25 (all U -contains_slb(create_slb,U)) # label(ax20) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	26 (all U all V all W all X all Y (pair_in_list(insert_slb(U,pair(V,X)),W,Y) <-> Y = X & V = W | pair_in_list(U,W,Y))) # label(ax23) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	27 (all U all V -pair_in_list(create_slb,U,V)) # label(ax22) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	28 (all U all V all W all X (V != W & contains_slb(U,W) -> lookup_slb(U,W) = lookup_slb(insert_slb(U,pair(V,X)),W))) # label(ax27) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	29 (all U all V all W all X (-contains_slb(V,X) -> remove_cpq(triple(U,V,W),X) = triple(U,V,bad))) # label(ax43) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	30 (all U all V all W all X (contains_cpq(triple(U,V,W),X) <-> contains_slb(V,X))) # label(ax39) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	31 (all U all V findmin_cpq_res(triple(U,create_slb,V)) = bottom) # label(ax50) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	32 (all U all V all W (-ok(triple(U,V,W)) -> bad = W)) # label(ax41) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	33 (all U all V all W (succ_cpq(U,V) -> succ_cpq(U,insert_cpq(V,W)))) # label(ax32) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	34 (all U succ_cpq(U,U)) # label(ax31) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	35 (all U removemin_cpq_res(U) = findmin_cpq_res(U)) # label(ax53) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	36 (all U all V all W all X (V != create_slb -> findmin_pqp_res(U) = findmin_cpq_res(triple(U,V,W)))) # label(ax51) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	37 (all U all V all W all X triple(insert_pqp(U,X),insert_slb(V,pair(X,bottom)),W) = insert_cpq(triple(U,V,W),X)) # label(ax42) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	38 (all U all V all W all X (contains_slb(V,X) & strictly_less_than(X,lookup_slb(V,X)) -> triple(remove_pqp(U,X),remove_slb(V,X),bad) = remove_cpq(triple(U,V,W),X))) # label(ax45) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	39 (all U all V (succ_cpq(U,V) -> succ_cpq(U,removemin_cpq_eff(V)))) # label(ax35) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	40 (all U all V all W all X (-contains_slb(V,findmin_pqp_res(U)) & V != create_slb -> triple(U,update_slb(V,findmin_pqp_res(U)),bad) = findmin_cpq_eff(triple(U,V,W)))) # label(ax47) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	41 (all U all V (ok(triple(U,V,bad)) <-> $F)) # label(ax40) # label(axiom) # label(non_clause).  [assumption].
0.84/1.15	42 (all U all V all W all X (less_than(lookup_slb(V,X),X) & contains_slb(V,X) -> remove_cpq(triple(U,V,W),X) = triple(remove_pqp(U,X),remove_slb(V,X),W))) # label(ax44) # label(axiom) # label(non_clause).  [assumption].
0.84/1.16	43 (all U all V all W all X (V != create_slb & contains_slb(V,findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U),lookup_slb(V,findmin_pqp_res(U))) -> triple(U,update_slb(V,findmin_pqp_res(U)),bad) = findmin_cpq_eff(triple(U,V,W)))) # label(ax48) # label(axiom) # label(non_clause).  [assumption].
0.84/1.16	44 (all U all V all W all X all Y (less_than(Y,X) -> (check_cpq(triple(U,V,W)) <-> check_cpq(triple(U,insert_slb(V,pair(X,Y)),W))))) # label(ax37) # label(axiom) # label(non_clause).  [assumption].
0.84/1.16	45 (all U all V check_cpq(triple(U,create_slb,V))) # label(ax36) # label(axiom) # label(non_clause).  [assumption].
0.84/1.16	46 (all U all V all W (succ_cpq(U,V) -> succ_cpq(U,remove_cpq(V,W)))) # label(ax33) # label(axiom) # label(non_clause).  [assumption].
0.84/1.16	47 (all U all V (succ_cpq(U,V) -> succ_cpq(U,findmin_cpq_eff(V)))) # label(ax34) # label(axiom) # label(non_clause).  [assumption].
0.84/1.16	48 (all U removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U),findmin_cpq_res(U))) # label(ax52) # label(axiom) # label(non_clause).  [assumption].
0.84/1.16	49 (all U all V findmin_cpq_eff(triple(U,create_slb,V)) = triple(U,create_slb,bad)) # label(ax46) # label(axiom) # label(non_clause).  [assumption].
0.84/1.16	50 (all U all V all W all X all Y (strictly_less_than(X,Y) -> (check_cpq(triple(U,insert_slb(V,pair(X,Y)),W)) <-> $F))) # label(ax38) # label(axiom) # label(non_clause).  [assumption].
0.84/1.16	51 (all U all V all W all X (create_slb != V & less_than(lookup_slb(V,findmin_pqp_res(U)),findmin_pqp_res(U)) & contains_slb(V,findmin_pqp_res(U)) -> triple(U,update_slb(V,findmin_pqp_res(U)),W) = findmin_cpq_eff(triple(U,V,W)))) # label(ax49) # label(axiom) # label(non_clause).  [assumption].
0.84/1.16	52 (all U all V (contains_pq(U,V) <-> pi_sharp_remove(U,V))) # label(ax56) # label(axiom) # label(non_clause).  [assumption].
0.84/1.16	53 (all U all V (pi_sharp_removemin(U,V) <-> issmallestelement_pq(U,V) & contains_pq(U,V))) # label(ax60) # label(axiom) # label(non_clause).  [assumption].
0.84/1.16	54 (all U all V i(triple(U,create_slb,V)) = create_pq) # label(ax54) # label(axiom) # label(non_clause).  [assumption].
0.84/1.16	55 (all U ((exists V pi_sharp_find_min(i(U),V)) <-> pi_find_min(U))) # label(ax59) # label(axiom) # label(non_clause).  [assumption].
0.84/1.16	56 (all U all V all W all X all Y i(triple(U,insert_slb(V,pair(X,Y)),W)) = insert_pq(i(triple(U,V,W)),X)) # label(ax55) # label(axiom) # label(non_clause).  [assumption].
0.84/1.16	57 (all U all V (pi_sharp_remove(i(U),V) <-> pi_remove(U,V))) # label(ax57) # label(axiom) # label(non_clause).  [assumption].
0.84/1.16	58 (all U ((exists V (succ_cpq(U,V) & ok(V) & check_cpq(V))) <-> phi(U))) # label(ax62) # label(axiom) # label(non_clause).  [assumption].
0.84/1.16	59 (all U all V (contains_pq(U,V) & issmallestelement_pq(U,V) <-> pi_sharp_find_min(U,V))) # label(ax58) # label(axiom) # label(non_clause).  [assumption].
0.84/1.16	60 (all U (pi_removemin(U) <-> (exists V pi_sharp_find_min(i(U),V)))) # label(ax61) # label(axiom) # label(non_clause).  [assumption].
0.84/1.16	61 (all U all V all W (phi(findmin_cpq_eff(triple(U,V,W))) -> pi_sharp_find_min(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W))))) # label(main4_l7) # label(lemma) # label(non_clause).  [assumption].
0.84/1.16	62 -(all U all V all W (pi_find_min(triple(U,V,W)) -> (phi(findmin_cpq_eff(triple(U,V,W))) -> (exists X (findmin_cpq_res(triple(U,V,W)) = findmin_pq_res(i(triple(U,V,W)),X) & pi_sharp_find_min(i(triple(U,V,W)),X)))))) # label(co4) # label(negated_conjecture) # label(non_clause).  [assumption].
0.84/1.16	
0.84/1.16	============================== end of process non-clausal formulas ===
0.84/1.16	
0.84/1.16	============================== PROCESS INITIAL CLAUSES ===============
0.84/1.16	
0.84/1.16	============================== PREDICATE ELIMINATION =================
0.84/1.16	63 pi_sharp_find_min(i(A),f2(A)) | -pi_find_min(A) # label(ax59) # label(axiom).  [clausify(55)].
0.84/1.16	64 pi_find_min(triple(c1,c2,c3)) # label(co4) # label(negated_conjecture).  [clausify(62)].
0.84/1.16	65 -pi_sharp_find_min(i(A),B) | pi_find_min(A) # label(ax59) # label(axiom).  [clausify(55)].
0.84/1.16	Derived: pi_sharp_find_min(i(triple(c1,c2,c3)),f2(triple(c1,c2,c3))).  [resolve(63,b,64,a)].
0.84/1.16	Derived: pi_sharp_find_min(i(A),f2(A)) | -pi_sharp_find_min(i(A),B).  [resolve(63,b,65,b)].
0.84/1.16	66 -contains_pq(A,B) | less_than(C,B) | -issmallestelement_pq(A,C) # label(ax10) # label(axiom).  [clausify(9)].
0.84/1.16	67 contains_pq(A,f1(A,B)) | issmallestelement_pq(A,B) # label(ax10) # label(axiom).  [clausify(9)].
0.84/1.16	68 -pi_sharp_removemin(A,B) | issmallestelement_pq(A,B) # label(ax60) # label(axiom).  [clausify(53)].
0.84/1.16	69 issmallestelement_pq(A,B) | -pi_sharp_find_min(A,B) # label(ax58) # label(axiom).  [clausify(59)].
0.84/1.16	70 -less_than(A,f1(B,A)) | issmallestelement_pq(B,A) # label(ax10) # label(axiom).  [clausify(9)].
0.84/1.16	Derived: -contains_pq(A,B) | less_than(C,B) | contains_pq(A,f1(A,C)).  [resolve(66,c,67,b)].
0.84/1.16	Derived: -contains_pq(A,B) | less_than(C,B) | -pi_sharp_removemin(A,C).  [resolve(66,c,68,b)].
0.84/1.16	Derived: -contains_pq(A,B) | less_than(C,B) | -pi_sharp_find_min(A,C).  [resolve(66,c,69,a)].
0.84/1.16	Derived: -contains_pq(A,B) | less_than(C,B) | -less_than(C,f1(A,C)).  [resolve(66,c,70,b)].
0.84/1.16	71 pi_sharp_removemin(A,B) | -issmallestelement_pq(A,B) | -contains_pq(A,B) # label(ax60) # label(axiom).  [clausify(53)].
0.84/1.16	Derived: pi_sharp_removemin(A,B) | -contains_pq(A,B) | contains_pq(A,f1(A,B)).  [resolve(71,b,67,b)].
0.84/1.16	Derived: pi_sharp_removemin(A,B) | -contains_pq(A,B) | -pi_sharp_find_min(A,B).  [resolve(71,b,69,a)].
0.84/1.16	Derived: pi_sharp_removemin(A,B) | -contains_pq(A,B) | -less_than(B,f1(A,B)).  [resolve(71,b,70,b)].
0.84/1.16	72 -contains_pq(A,B) | -issmallestelement_pq(A,B) | pi_sharp_find_min(A,B) # label(ax58) # label(axiom).  [clausify(59)].
0.84/1.16	Derived: -contains_pq(A,B) | pi_sharp_find_min(A,B) | contains_pq(A,f1(A,B)).  [resolve(72,b,67,b)].
0.84/1.16	Derived: -contains_pq(A,B) | pi_sharp_find_min(A,B) | -pi_sharp_removemin(A,B).  [resolve(72,b,68,b)].
0.84/1.16	Derived: -contains_pq(A,B) | pi_sharp_find_min(A,B) | -less_than(B,f1(A,B)).  [resolve(72,b,70,b)].
0.84/1.16	73 -issmallestelement_pq(A,B) | -contains_pq(A,B) | findmin_pq_eff(A,B) = A # label(ax13) # label(axiom).  [clausify(6)].
0.84/1.16	Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | contains_pq(A,f1(A,B)).  [resolve(73,a,67,b)].
0.84/1.16	Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -pi_sharp_removemin(A,B).  [resolve(73,a,68,b)].
0.84/1.16	Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -pi_sharp_find_min(A,B).  [resolve(73,a,69,a)].
0.84/1.16	Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -less_than(B,f1(A,B)).  [resolve(73,a,70,b)].
0.84/1.16	74 -issmallestelement_pq(A,B) | -contains_pq(A,B) | removemin_pq_res(A,B) = B # label(ax16) # label(axiom).  [clausify(8)].
0.84/1.16	Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | contains_pq(A,f1(A,B)).  [resolve(74,a,67,b)].
0.84/1.16	Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | -pi_sharp_removemin(A,B).  [resolve(74,a,68,b)].
0.84/1.16	Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | -pi_sharp_find_min(A,B).  [resolve(74,a,69,a)].
0.84/1.16	Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | -less_than(B,f1(A,B)).  [resolve(74,a,70,b)].
0.84/1.16	75 -issmallestelement_pq(A,B) | -contains_pq(A,B) | findmin_pq_res(A,B) = B # label(ax14) # label(axiom).  [clausify(11)].
0.84/1.16	Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | contains_pq(A,f1(A,B)).  [resolve(75,a,67,b)].
0.84/1.16	Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -pi_sharp_removemin(A,B).  [resolve(75,a,68,b)].
0.84/1.16	Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -pi_sharp_find_min(A,B).  [resolve(75,a,69,a)].
0.84/1.16	Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -less_than(B,f1(A,B)).  [resolve(75,a,70,b)].
0.84/1.16	76 -issmallestelement_pq(A,B) | -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) # label(ax15) # label(axiom).  [clausify(10)].
0.84/1.16	Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | contains_pq(A,f1(A,B)).  [resolve(76,a,67,b)].
0.84/1.16	Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | -pi_sharp_removemin(A,B).  [resolve(76,a,68,b)].
0.84/1.16	Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | -pi_sharp_find_min(A,B).  [resolve(76,a,69,a)].
0.84/1.16	Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | -less_than(B,f1(A,B)).  [resolve(76,a,70,b)].
1.12/1.39	77 pi_sharp_removemin(A,B) | -contains_pq(A,B) | contains_pq(A,f1(A,B)).  [resolve(71,b,67,b)].
1.12/1.39	78 -pi_sharp_removemin(A,B) | contains_pq(A,B) # label(ax60) # label(axiom).  [clausify(53)].
1.12/1.39	79 -contains_pq(A,B) | less_than(C,B) | -pi_sharp_removemin(A,C).  [resolve(66,c,68,b)].
1.12/1.39	Derived: -contains_pq(A,B) | contains_pq(A,f1(A,B)) | -contains_pq(A,C) | less_than(B,C).  [resolve(77,a,79,c)].
1.12/1.39	80 pi_sharp_removemin(A,B) | -contains_pq(A,B) | -pi_sharp_find_min(A,B).  [resolve(71,b,69,a)].
1.12/1.39	Derived: -contains_pq(A,B) | -pi_sharp_find_min(A,B) | -contains_pq(A,C) | less_than(B,C).  [resolve(80,a,79,c)].
1.12/1.39	81 pi_sharp_removemin(A,B) | -contains_pq(A,B) | -less_than(B,f1(A,B)).  [resolve(71,b,70,b)].
1.12/1.39	Derived: -contains_pq(A,B) | -less_than(B,f1(A,B)) | -contains_pq(A,C) | less_than(B,C).  [resolve(81,a,79,c)].
1.12/1.39	82 -contains_pq(A,B) | pi_sharp_find_min(A,B) | -pi_sharp_removemin(A,B).  [resolve(72,b,68,b)].
1.12/1.39	Derived: -contains_pq(A,B) | pi_sharp_find_min(A,B) | -contains_pq(A,B) | contains_pq(A,f1(A,B)).  [resolve(82,c,77,a)].
1.12/1.39	83 -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -pi_sharp_removemin(A,B).  [resolve(73,a,68,b)].
1.12/1.39	Derived: -contains_pq(A,B) | findmin_pq_eff(A,B) = A | -contains_pq(A,B) | contains_pq(A,f1(A,B)).  [resolve(83,c,77,a)].
1.12/1.39	84 -contains_pq(A,B) | removemin_pq_res(A,B) = B | -pi_sharp_removemin(A,B).  [resolve(74,a,68,b)].
1.12/1.39	Derived: -contains_pq(A,B) | removemin_pq_res(A,B) = B | -contains_pq(A,B) | contains_pq(A,f1(A,B)).  [resolve(84,c,77,a)].
1.12/1.39	85 -contains_pq(A,B) | findmin_pq_res(A,B) = B | -pi_sharp_removemin(A,B).  [resolve(75,a,68,b)].
1.12/1.39	Derived: -contains_pq(A,B) | findmin_pq_res(A,B) = B | -contains_pq(A,B) | contains_pq(A,f1(A,B)).  [resolve(85,c,77,a)].
1.12/1.39	86 -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | -pi_sharp_removemin(A,B).  [resolve(76,a,68,b)].
1.12/1.39	Derived: -contains_pq(A,B) | removemin_pq_eff(A,B) = remove_pq(A,B) | -contains_pq(A,B) | contains_pq(A,f1(A,B)).  [resolve(86,c,77,a)].
1.12/1.39	87 -pi_removemin(A) | pi_sharp_find_min(i(A),f4(A)) # label(ax61) # label(axiom).  [clausify(60)].
1.12/1.39	88 pi_removemin(A) | -pi_sharp_find_min(i(A),B) # label(ax61) # label(axiom).  [clausify(60)].
1.12/1.39	Derived: pi_sharp_find_min(i(A),f4(A)) | -pi_sharp_find_min(i(A),B).  [resolve(87,a,88,a)].
1.12/1.39	89 pi_sharp_remove(i(A),B) | -pi_remove(A,B) # label(ax57) # label(axiom).  [clausify(57)].
1.12/1.39	90 -pi_sharp_remove(i(A),B) | pi_remove(A,B) # label(ax57) # label(axiom).  [clausify(57)].
1.12/1.39	91 contains_pq(A,B) | -pi_sharp_remove(A,B) # label(ax56) # label(axiom).  [clausify(52)].
1.12/1.39	92 -contains_pq(A,B) | pi_sharp_remove(A,B) # label(ax56) # label(axiom).  [clausify(52)].
1.12/1.39	
1.12/1.39	============================== end predicate elimination =============
1.12/1.39	
1.12/1.39	Auto_denials:  (non-Horn, no changes).
1.12/1.39	
1.12/1.39	Term ordering decisions:
1.12/1.39	Function symbol KB weights:  create_slb=1. bad=1. bottom=1. create_pq=1. c1=1. c2=1. c3=1. insert_slb=1. pair=1. insert_pq=1. update_slb=1. lookup_slb=1. remove_pq=1. remove_cpq=1. remove_slb=1. findmin_pq_eff=1. findmin_pq_res=1. removemin_pq_eff=1. removemin_pq_res=1. insert_cpq=1. remove_pqp=1. insert_pqp=1. f1=1. findmin_pqp_res=1. i=1. findmin_cpq_eff=1. findmin_cpq_res=1. removemin_cpq_eff=1. removemin_cpq_res=1. f2=1. f3=1. f4=1. triple=1.
1.12/1.39	
1.12/1.39	============================== end of process initial clauses ========
1.12/1.39	
1.12/1.39	============================== CLAUSES FOR SEARCH ====================
1.12/1.39	
1.12/1.39	============================== end of clauses for search =============
1.12/1.39	
1.12/1.39	============================== SEARCH ================================
1.12/1.39	
1.12/1.39	% Starting search at 0.03 seconds.
1.12/1.39	
1.12/1.39	============================== PROOF =================================
1.12/1.39	% SZS status Theorem
1.12/1.39	% SZS output start Refutation
1.12/1.39	
1.12/1.39	% Proof 1 at 0.25 (+ 0.01) seconds.
1.12/1.39	% Length of proof is 17.
1.12/1.39	% Level of proof is 4.
1.12/1.39	% Maximum clause weight is 28.000.
1.12/1.39	% Given clauses 442.
1.12/1.39	
1.12/1.39	11 (all U all V (issmallestelement_pq(U,V) & contains_pq(U,V) -> V = findmin_pq_res(U,V))) # label(ax14) # label(axiom) # label(non_clause).  [assumption].
1.12/1.39	59 (all U all V (contains_pq(U,V) & issmallestelement_pq(U,V) <-> pi_sharp_find_min(U,V))) # label(ax58) # label(axiom) # label(non_clause).  [assumption].
1.12/1.39	61 (all U all V all W (phi(findmin_cpq_eff(triple(U,V,W))) -> pi_sharp_find_min(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W))))) # label(main4_l7) # label(lemma) # label(non_clause).  [assumption].
1.12/1.39	62 -(all U all V all W (pi_find_min(triple(U,V,W)) -> (phi(findmin_cpq_eff(triple(U,V,W))) -> (exists X (findmin_cpq_res(triple(U,V,W)) = findmin_pq_res(i(triple(U,V,W)),X) & pi_sharp_find_min(i(triple(U,V,W)),X)))))) # label(co4) # label(negated_conjecture) # label(non_clause).  [assumption].
1.12/1.39	69 issmallestelement_pq(A,B) | -pi_sharp_find_min(A,B) # label(ax58) # label(axiom).  [clausify(59)].
1.12/1.39	75 -issmallestelement_pq(A,B) | -contains_pq(A,B) | findmin_pq_res(A,B) = B # label(ax14) # label(axiom).  [clausify(11)].
1.12/1.39	102 phi(findmin_cpq_eff(triple(c1,c2,c3))) # label(co4) # label(negated_conjecture).  [clausify(62)].
1.12/1.39	127 findmin_cpq_res(triple(c1,c2,c3)) != findmin_pq_res(i(triple(c1,c2,c3)),A) | -pi_sharp_find_min(i(triple(c1,c2,c3)),A) # label(co4) # label(negated_conjecture).  [clausify(62)].
1.12/1.39	128 findmin_pq_res(i(triple(c1,c2,c3)),A) != findmin_cpq_res(triple(c1,c2,c3)) | -pi_sharp_find_min(i(triple(c1,c2,c3)),A).  [copy(127),flip(a)].
1.12/1.39	133 contains_pq(A,B) | -pi_sharp_find_min(A,B) # label(ax58) # label(axiom).  [clausify(59)].
1.12/1.39	158 -phi(findmin_cpq_eff(triple(A,B,C))) | pi_sharp_find_min(i(triple(A,B,C)),findmin_cpq_res(triple(A,B,C))) # label(main4_l7) # label(lemma).  [clausify(61)].
1.12/1.39	182 -contains_pq(A,B) | findmin_pq_res(A,B) = B | -pi_sharp_find_min(A,B).  [resolve(75,a,69,a)].
1.12/1.39	261 pi_sharp_find_min(i(triple(c1,c2,c3)),findmin_cpq_res(triple(c1,c2,c3))).  [resolve(158,a,102,a)].
1.12/1.39	2063 -contains_pq(i(triple(c1,c2,c3)),findmin_cpq_res(triple(c1,c2,c3))) | findmin_pq_res(i(triple(c1,c2,c3)),findmin_cpq_res(triple(c1,c2,c3))) = findmin_cpq_res(triple(c1,c2,c3)).  [resolve(261,a,182,c)].
1.12/1.39	2067 contains_pq(i(triple(c1,c2,c3)),findmin_cpq_res(triple(c1,c2,c3))).  [resolve(261,a,133,b)].
1.12/1.39	2068 findmin_pq_res(i(triple(c1,c2,c3)),findmin_cpq_res(triple(c1,c2,c3))) != findmin_cpq_res(triple(c1,c2,c3)).  [resolve(261,a,128,b)].
1.12/1.39	2072 $F.  [back_unit_del(2063),unit_del(a,2067),unit_del(b,2068)].
1.12/1.39	
1.12/1.39	% SZS output end Refutation
1.12/1.39	============================== end of proof ==========================
1.12/1.39	
1.12/1.39	============================== STATISTICS ============================
1.12/1.39	
1.12/1.39	Given=442. Generated=4441. Kept=1968. proofs=1.
1.12/1.39	Usable=440. Sos=1444. Demods=60. Limbo=5, Disabled=206. Hints=0.
1.12/1.39	Megabytes=3.92.
1.12/1.39	User_CPU=0.25, System_CPU=0.01, Wall_clock=1.
1.12/1.39	
1.12/1.39	============================== end of statistics =====================
1.12/1.39	
1.12/1.39	============================== end of search =========================
1.12/1.39	
1.12/1.39	THEOREM PROVED
1.12/1.39	% SZS status Theorem
1.12/1.39	
1.12/1.39	Exiting with 1 proof.
1.12/1.39	
1.12/1.39	Process 24319 exit (max_proofs) Thu Aug 29 09:19:23 2019
1.12/1.39	Prover9 interrupted
1.12/1.39	EOF